Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

Q: sin x dx cos5x b.

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Q: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: Find the Absolute Extremum of F(x)=2sinx-cos2x over [0,2pi]

A: Consider the following:  Differentiate the function and find critical point:…

Q: Let a be a constant, Evaluate[ (a* + x² + a) sin(3z") + 15z*)dzr.

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: Obtain graphically an approximately value of the root of x = sin x + Tt /2

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: Use the Substitution Rule to provethat∫cos2ax dx =(x/2) +(sin(2ax)/4a) + C.

A: The given integral is ∫cos2axdx=x2+sin2ax4a+C

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

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Q: Integrate with respect to x, the square root of (1-cos5x)/2

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Q: Evaluate the integral ∫sin (2t + 1)/cos2 (2t + 1) dt

A: Given information: ∫sin2t+1cos22t+1dt

Q: 11.. , Evaluate each definite integral. a) cos² x sin x dx

A: Use substitutions to integrate

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: f(x) = cos (In (3x))

A:

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: Consider - Vx2-9 x3 dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: To solve a certain type of complex integrals we usually simplify them using basic trigonometric…

Q: Q2: Derive the reduction formulas of f sin"xcos™x dx? Using this solve the S sin*xcos³x dx.

A: Given: ∫sin4x cos5x dx

Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

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Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: X has a solution in Use the Intermediate Value Theorem to show that cos(x) (0, - 2

A: Using Intermediate Value Theorem to show that cos(x) =x is a solution in0,π2.

Q: If g(x): = cos 2x and f(x) = sin-n, find g(f(x)). %3D

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Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

A: Given: fx=sinxcos3xf'x=cos4x-2sinxsin3x To find: f''π3=?f'''π3=? Formulas used:…

Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: Find all values of in the interval 0, 2 such that sin x = sin 2x

A: To find all values in the interval for the function

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: Evaluate the integral. 2 sin -1 x dx

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Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Using an appropriate substitution, f sin®(x)cos³(x)dx is equal to:

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫x sin (2x2) dx, u = 2x2

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Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…

Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx